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Mat. Tr., 2017, Volume 20, Number 1, Pages 145–157 (Mi mt319)  

On a property of the Legendre transform

A. A. Mogul'skiĭab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: For a pair of convex lower semicontinuous functions connected by the Legendre transform, we establish that their derivatives are mutually inverse functions (in the generalized sense).

Key words: deviation rate function, logarithm of the Laplace transform, Legendre transform, generalized inverse function.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00220_а


DOI: https://doi.org/10.17377/mattrudy.2017.20.109

Full text: PDF file (176 kB)
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English version:
Siberian Advances in Mathematics, 2018, 28:1, 65–73

Document Type: Article
UDC: 519.21
Received: 03.05.2016

Citation: A. A. Mogul'skiǐ, “On a property of the Legendre transform”, Mat. Tr., 20:1 (2017), 145–157; Siberian Adv. Math., 28:1 (2018), 65–73

Citation in format AMSBIB
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\by A.~A.~Mogul'ski{\v\i}
\paper On a property of the Legendre transform
\jour Mat. Tr.
\yr 2017
\vol 20
\issue 1
\pages 145--157
\mathnet{http://mi.mathnet.ru/mt319}
\crossref{https://doi.org/10.17377/mattrudy.2017.20.109}
\elib{http://elibrary.ru/item.asp?id=29145407}
\transl
\jour Siberian Adv. Math.
\yr 2018
\vol 28
\issue 1
\pages 65--73
\crossref{https://doi.org/10.3103/S1055134418010066}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043499222}


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